In a series of papers [1]}, [2]}, [3]} we have investigated
operator-algebraic methods based on conformal field theory to construct quantum
field models on two-dimensional spacetime with a weak localization property.
Although we succeeded to obtain various
examples and general structural results, there was missing one important property:
strict localization. In the present paper we construct further new families of quantum
field models and prove their strict locality. In other words, we construct interacting
two-dimensional Haag-Kastler nets, using techniques from conformal nets.
